I haven't researched this at all, but I assume "o clock" must have started as "on the clock". As in "It's 10 minutes and 23 seconds on the clock".
How to settle the argument you're all having, I have no idea - we should divert to the wisdom of Fellippe, whom has a better command of English than most native speakers and patently *everyone* not from the northeast.
O’clock is used when the primary hour is in use.
One o’clock. Two o’clock.
One thirty doesn’t have o’clock. Verbally, “half past one” doesn’t need it, but I was always taught when writing, the rule is to follow the hour, so it’s “half past one o’clock” written.
Of course, writing rules change over time, and with the invention of text messages and mobile keyboards, a lot of those older rules are fading away. Take “okay” for an example. It used to be “okay”, but that was too much writing, so it became “OK”. Now, it’s often just “K”.
How I was taught 40 yrs ago may very well not be the same rule for the kids of today. In the end, it’s not a big deal one way or another, and mainly a matter of personal preference — unless, of course, somebody is paying you to code it. Then you follow their instructions, no matter how odd you might find them to be. Paychecks trump personal preference, as I’ve had to deal with in writing. To get a short story published in a local magazine, I had to change the word “niggerly” to “miserly”, because they found it “racist”. (Insert loooooong sigh here.)
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@Pete: We don’t hear “three-quarters past”, but we do hear, “quarter till”. ;)